""" Pareto Filter -- finds non-dominated cases. """
# pylint: disable-msg=E0611,F0401
from openmdao.main.datatypes.api import Slot, List, Str
from openmdao.lib.casehandlers.api import CaseSet, caseiter_to_caseset
from openmdao.main.component import Component
from openmdao.main.interfaces import ICaseIterator
[docs]class ParetoFilter(Component):
"""Takes a set of cases and filters out the subset of cases which are
pareto optimal. Assumes that smaller values for model responses are
better, so all problems must be posed as minimization problems.
"""
# pylint: disable-msg=E1101
criteria = List(Str, iotype="in",
desc="List of outputs from the case to consider for "
"filtering. Note that only case outputs are allowed as "
"criteria.")
#case_set = Slot(ICaseIterator, iotype="in",
# desc="CaseIterator with the cases to be filtered to "
# "Find the pareto optimal subset.")
case_sets = List(Slot(ICaseIterator), value=[], iotype="in",
desc="CaseSet with the cases to be filtered to "
"find the pareto optimal subset.")
pareto_set = Slot(CaseSet, iotype="out",
desc="Resulting collection of pareto optimal cases.", copy="shallow")
dominated_set = Slot(CaseSet, iotype="out",
desc="Resulting collection of dominated cases.", copy="shallow")
def _is_dominated(self, y1, y2):
"""Tests to see if the point y1 is dominated by the point y2.
True if y1 is dominated by y2, False otherwise.
"""
if y1 == y2:
return False
for a, b in zip(y1, y2):
if a < b:
return False
return True
[docs] def execute(self):
"""Finds and removes pareto optimal points in the given case set.
Returns a list of pareto optimal points. Smaller is better for all
criteria.
"""
#convert stuff to caseSets if they are not
case_sets = []
for ci in self.case_sets:
if not isinstance(ci, CaseSet):
case_sets.append(caseiter_to_caseset(ci))
else:
case_sets.append(ci)
y_list = []
if len(case_sets) > 1:
case_set = case_sets[0].union(*case_sets[1:])
else:
case_set = case_sets[0]
criteria_count = len(self.criteria)
try:
# need to transpose the list of outputs
y_list = zip(*[case_set[crit] for crit in self.criteria])
except KeyError:
self.raise_exception('no cases provided had all of the outputs '
'matching the provided criteria, %s' % self.criteria, ValueError)
y_temp = list(y_list)
self.dominated_set = CaseSet()
self.pareto_set = CaseSet() # TODO: need a way to copy casesets
for point1, case in zip(y_list, iter(case_set)):
dominated = False
for point2 in y_temp:
if self._is_dominated(point1, point2):
self.dominated_set.record(case)
y_temp.remove(point1)
dominated = True
break
if not dominated:
self.pareto_set.record(case)
if __name__ == "__main__": # pragma: no cover
# pylint: disable-msg=C0103, E1101
from matplotlib import pyplot as py
from mpl_toolkits.mplot3d import Axes3D
from numpy import random
random.seed(10)
from openmdao.main.case import Case
pf = ParetoFilter()
# 2D PARETO FILTERING EXAMPLE
n = 1000
x = random.uniform(-1, 0, n)
y = -(1 - x**2)**0.5 * random.random(n)
cases = CaseSet()
for x_0, y_0 in zip(x, y):
cases.record(Case(inputs=[("x", x_0), ("y", y_0)]))
pf.case_sets = [cases]
pf.criteria = ['x', 'y']
pf.execute()
x_p, y_p = pf.pareto_set['x'], pf.pareto_set['y']
x_dom, y_dom = pf.dominated_set['x'], pf.dominated_set['y']
py.figure()
py.scatter(x, y, s=5)
py.scatter(x_dom, y_dom, c='', edgecolor='b', s=80)
py.scatter(x_p, y_p, c='', edgecolors='r', s=80)
#3D PARETO FILTERING EXAMPLE
n = 1000
x = random.uniform(-1, 0, n)
y = -(1 - x**2)**0.5 * random.random(n)
z = -(1 - x**2 - y**2)**0.5 * random.random(n)
doe = zip(x, y, z)
pf.criteria = ['x', 'y', 'z']
cases = CaseSet()
for x_0, y_0, z_0 in zip(x, y, z):
cases.record(Case(inputs=[("x", x_0),
("y", y_0),
("z", z_0)]))
pf.case_sets = [cases]
pf.execute()
x_p, y_p, z_p = pf.pareto_set['x'], pf.pareto_set['y'], pf.pareto_set['z']
x_dom, y_dom, z_dom = pf.dominated_set['x'], pf.dominated_set['y'], pf.dominated_set['z']
fig1 = py.figure()
a1 = Axes3D(fig1)
a1.scatter(x_dom, y_dom, z_dom, c='b')
a1.scatter(x_p, y_p, z_p, c='r', edgecolor='r')
py.show()
